Autopsy of SARS-CoV-2 spread dynamics in Ecuador using data assimilation techniques: A tale of two provinces

In this article, we considered a Bayesian approach to estimating the evolution of the COVID-19 pandemic in Ecuador, providing the first rigorous analysis of its progression in the country. Specifically, we applied variational data assimilation to estimate the parameters and initial conditions of a compartmental SARS-CoV-2 propagation model while accounting for structural data uncertainty through error covariance matrices. These optimized parameters correspond to maximum-a-posteriori (MAP) estimates, which, in a second stage, allow us to infer the posterior distribution of the parameters. We considered two different data sources: the official count of positive COVID-19 tests from the Ecuadorian Public Health Ministry (MSP) and an estimate of COVID-19-related deaths derived from excess mortality data recorded by the Ecuadorian Civil Registry (RC). We regard RC data as the closest approximation to the actual number of COVID-19 cases. The results highlight that, although there are differences between the estimates obtained using MSP data-generated in real time during the pandemic-and those based on positive cases inferred from excess mortality, the trends in the computed effective reproduction numbers coincide. This suggests that the methodology presented in this paper, and applied in real time during the pandemic, was able to accurately capture the evolution of the pandemic in Ecuador. Additionally, we conducted a comparative analysis of Ecuador's two most populous provinces, Pichincha and Guayas, which experienced the pandemic very differently, particularly in its initial stages. This study aimed to improve our understanding of the virus's spread in these provinces and provide insights into how epidemiological dynamics can vary within the same country.